Three people go for a morning walk together. Their steps measure 56 cm, 98 cm and 105 cm respectively. What is the minimum distance traveled when their steps will exactly match after starting the walk assuming that their walking speed is same?

A.	64.68 m
B.	0.07 m
C.	58.8 m
D.	52.92 m

If $\alpha$ and $\beta$ are the zeros of polynomial $x^2-x-2,$ find a polynomial whose zeros are $\dfrac{ \alpha^2 }{ \beta^2 }$ and $\dfrac{ \beta^2 }{ \alpha^2 }.$

A.	$k \left( x^2 + \dfrac{ 19 } { 4 }x + 1 \right)$
B.	$k \left( x^2 + \dfrac{ 17 } { 4 }x + 1 \right)$
C.	$k \left( x^2 - \dfrac{ 19 } { 4 }x + 1 \right)$
D.	$k \left( x^2 - \dfrac{ 17 } { 4 }x + 1 \right)$

A sailer can row $30{\space} km$ downstream in $2{\space} hours$ and $14{\space} km$ upstream in $4 {\space}hours$. Find the speed of the sailer in still water.

A.	$14.25{\space} km/h$
B.	$19.25{\space} km/h$
C.	$9.25{\space} km/hr$
D.	None of these

The sum of a number and its reciprocal is $\dfrac { 25 } { 12 }$. Find the number.

A.	$\dfrac { 3 } { 5 }$ or $\dfrac { 5 } { 3 }$
B.	$\dfrac { 2 } { 5 }$ or $\dfrac { 5 } { 2 }$
C.	$\dfrac { 3 } { 4 }$ or $\dfrac { 4 } { 3 }$
D.	$\dfrac { 2 } { 4 }$ or $\dfrac { 4 } { 2}$

The number of integers between $207$ and $2021$ ending with $6$ is

A.	$183$
B.	$188$
C.	$191$
D.	$181$

In a trapezium $ABCD$ , $O$ is the point of intersection of $AC$ and $BD$. $AB || CD$ and $AB = 2 \times CD$. If the area of $\Delta AOB = 72 \space cm^2$, find the area of $\Delta COD$.

A.	$19 \space cm^2$
B.	$21 \space cm^2$
C.	$20 \space cm^2$
D.	$18 \space cm^2$

Find the coordinates of the midpoint of the line segment joining the points $A(-15, -12)$ and $B(-11, -10)$.

A.	$(-13 , -11)$
B.	$(-3 , -1)$
C.	$(-12 , -10)$
D.	$(-14 , -12)$

Simplify: $\cot^2 \theta \left( \dfrac{ \sec \theta - 1 } { 1 + \sin \theta } \right) + \sec^2 \theta \left( \dfrac{ \sin\theta - 1 } { 1 + \sec \theta } \right)$

A.	$sin\theta cos\theta$
B.	$1$
C.	$0$
D.	$1 + sin\theta cos\theta$

If the lengths of tangents drawn from an external point $A$ to a point $P$ and $Q$ on the circle are equal then $AP$ is equal to:

A.	$AQ$
B.	$OQ$
C.	$OP$
D.	$OA$

A.
B.
C.
D.

Find the area of the square that can be inscribed in a circle of radius $5 \space cm$.

A.	$70 \space cm^2$
B.	$50 \space cm^2$
C.	$10 \space cm^2$
D.	$\text { None of these }$

The perimeters of the ends of the frustum of a cone are $8.36 \space cm$ and $11 \space cm$. If the height of the frustum is $29 \space cm$, find its curved surface area. (Take $\pi = \dfrac { 22 } { 7 }$).

A.	$280.72 \space cm^2$
B.	$9.68 \space cm^2$
C.	$89.32 \space cm^2$
D.	$\text { None of these }$

Find the mean of the following data

Class interval	0-10	10-20	20-30	30-40	40-50
Frequency	10	16	10	25	39

.

A.	41.7
B.	36.7
C.	31.7
D.	21.7

Aksana and Maksim sit on the 6-member board of directors for company P. If the board is to be split up into two 3-person subcommittees, what is the percentage that Maksim and Aksana are included in the same sub-committee?

A.	55%
B.	54%
C.	49%
D.	40%

If $cos \space \alpha = \dfrac{ 1 }{ 2 }$ and $tan \space \beta = 1 (0^\circ < \alpha < 90^\circ$ and $0^\circ < \beta < 90^\circ),$ find value of $sin \space 2(\alpha-\beta).$

A.	$\dfrac{ 1 }{ \sqrt{ 2 } }$
B.	$\dfrac { \sqrt{ 3 } } { 2 }$
C.	$\dfrac{ 1 }{ 2 }$
D.	$1$

Faces of a cube are marked with A,B,C,D,E and F. If two views of cube are as shown below, what will be there on the face opposite to face A ?

A.	B
B.	F
C.	C
D.	Cannot be determined

In this diagram, the triangle represents men, the square represents inspectors and the circle represents sports persons. Find the number of inspectors who are sports persons but not men.

A.	5
B.	8
C.	4
D.	6

Find the next term of given sequence ..
714, 645, 576, 507, 438, 369, 300, ....

A.	239
B.	225
C.	162
D.	231

Which of the following is the next terms in the series given below?
BXD, FTG, JPJ, NLM, ___

A.	RGP
B.	MHP
C.	QHQ
D.	RHP

Which of the following is the next term in the series:
D, G, H, K, L, O, P, ___

A.	S
B.	U
C.	R
D.	Q